Membrane phenomena as they relate to the function of nerve cells and their axons are being investigated from the view of basic kinetic processes associated with ion conduction. At the simplest and most defined level, the lipid bilayer is used as a model for chemical, electrical and optical probes of internal structures. Ionophores with known properties in bilayers are used to study transport processes in nerve cell bodies. By examination of the complex electrical behavior of urinary bladder and the crystalline lens, these inexcitable tissues constitute membrane systems for understanding cell-to-cell interactions and geometrical factors which complicate description of ion conduction in tissues. A new, rapid, stochastic method for linear analysis is used to obtain a complete description of ionic and charge movement processes in single nerve fibers of frog and crayfish which enhances interpretations of ion "channel" kinetics from measurements of spontaneous fluctuations. Optical probes of membrane potential fluctuations, together with linear analysis, provide microscopic information about conduction in crayfish axons. Spectral analysis of natural and transmitter-induced noise in nerve cell bodies is the basis for characterization of conduction in this membrane. At a most advanced level of complexity, the degree of nonlinearity of the input-output relationship of retinal neurons is assessed by evaluation of Wiener kernels and together with morphological identification provide structure-function relationships.